 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2011/m/m5/a/ii/solution

{0, 1, \dots, N}

. In this increasing ordering, the transition matrix is specified by

P_{00} = 1, P_{kj} = \frac{1}{k} (k \geq 1, 0 \leq j < k), P_{kj} = 0 otherwise .

For each positive

k

, the

k

possible amounts taken correspond bijectively to the

k

possible remaining counts. Each positive-state row therefore sums to one.

 New to topics? Read the docs here!